# Full text of "Analytical Mechanics"

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```EQUILIBRIUM OF A PARTICLE
23
4.   Frictional force is independent of the area of contact.
5.   The static frictional force which comes into play is not greater than that which is necessary to keep the body in equilibrium.
6.   Kinetic friction is smaller than static friction.
Laws 1 to 4 hold true for both static and kinetic friction. The coefficient of friction between two bodies depends upon. the condition of surfaces in contact.   Therefore the value of fj, is not a perfectly definite constant for a given pair of substances in contact.
The values given in the following table are averages of values obtained by several experimenters.
Mute rials in contact.	Condition of Hurfucen in contact.	Coefficient of friction.
Static.	Kinetic.
Wood on wood	Dry Wet Polished and greased Dry Wot Dry ({reused Wet	.50 .08 .35 .00 .SO .24 .15 .05 .30	.36 .25 .12 .40 .35 .18 .13
Wood on wood      .      ...
Wood on wood ...............
Hciivy rope on wood
Heavy rope on wood .......... Gust iron on ciist iron  .....
Cast iron on cast iron .........
Cnst iron on oak
Leather on cast iron ..........

ILLUSTRATIVE EXAMPLES.
1. A body which is on a rough horizontal floor can be brought to the point of motion by a force which makes an angle a with the floor.   Find the reaction of the floor and the coefficient of friction. The body is acted upon by three forces, Fig. IS, P, the given force, W, the weight of the body, R, the reaction of the floor.
Replacing R by its components F and N, and applying the conditions of equilibrium, we obtain
SZ m P cos a - F = 0,
Therefore
F = P cos a,
Jf = W - P sin a,```